Automatic implementation of material laws: Jacobian calculation in a finite element code with TAPENADE

• Main Authors: Zwicke, Florian, Knechtges, Philipp, Behr, Marek, Elgeti, Stefanie
• Format: Journal Article
• Language: English
• Published: 21-02-2017
• Subjects: Computer Science - Data Structures and Algorithms; Computer Science - Numerical Analysis; Physics - Fluid Dynamics
• DOI: 10.48550/arxiv.1702.06365

Computers & Mathematics with Applications, 72 (2016) 2808-2822 In an effort to increase the versatility of finite element codes, we explore
the possibility of automatically creating the Jacobian matrix necessary for the
gradient-based solution of nonlinear systems of equations. Particularly, we aim
to assess the feasibility of employing the automatic differentiation tool
TAPENADE for this purpose on a large Fortran codebase that is the result of
many years of continuous development. As a starting point we will describe the
special structure of finite element codes and the implications that this code
design carries for an efficient calculation of the Jacobian matrix. We will
also propose a first approach towards improving the efficiency of such a
method. Finally, we will present a functioning method for the automatic
implementation of the Jacobian calculation in a finite element software, but
will also point out important shortcomings that will have to be addressed in
the future.